The Mathematics game - Pi & Euler's identity
15cos(pi) + isin(pi) = -1 + i0 = -1. This is because the cosine and sine functions of pi are equal to their respective negative values since pi is half of the period of these functions.
In a right-angle triangle, sin(θ) is the ratio of the opposite(perpendicular) side to the hypotenuse, while cos(θ) is the ratio of the base(adjacent) side to the hypotenuse.
π = 180º and π/2 = 90º
Using trigonometric identity, sin θ = cos (90º - θ) and cos θ = sin (90º - θ)
sin (π) = cos (π /2 - π) = cos (-π /2) = 0
∴ sin (π) = -0 or 0
cos (π) = sin (π /2 - π) = sin (-π /2) = -1
∴ cos(π) = -1
Thus, the value of sin π is 0 and cos π is -1.
The central mathematical fact that we are interested in here is generally called
“Euler’s formula”, and written as eiθ = cos θ + isin θ
#mathematics #games #universe #eulertheorem
This video is the best Youtube Video I have seen in my life and I am just astonished by it and makes my inner curiosity rise again about the grand design of this Universe, and what could be a better subject than Mathematics for that. Please watch the original video from the actual creator [Alan Becker & his animator] of this masterpiece -
Source - https://www.youtube.com/watch?v=B1J6Ou4q8vE&t=708s&ab_channel=AlanBecker